This invention relates to retrofocus wide angle photographic objectives, and more particularly to such objectives that are corrected primarily for distortion by employing a non-spherical lens element with other lens elements which compensate other aberrations than distortion and that this compensation operates particularly effectively for astigmatism.
Various types of retrofocus wide angle lens objectives have been developed and are commonly characterized by the capability of providing a sufficiently long back focus length, but conversely, because of the asymmetrical form of the lens system itself, characterized by a lack of a suitable correction for distortion and either of astigmatism and coma. Particularly simultaneous good correction for both of distortion and astigmatism has been considered extremely difficult to achieve. To overcome this defect in aberrational problems, the necessary number of lens elements is unavoidably increased.
As a method of facilitating aberrational correction without causing a large increase in the complexity of the lens system, it is known to introduce a non-spherical surface to the lens system for distortional correction, provided that the position of the non-spherical surface is reasonably controlled as the introduction of the non-spherical surface affects other aberrations to a very large extent. For better distortional correction, it is preferred to locate the non-spherical surface at a point where off-axis principal light rays of the maximum image angle are incident thereon as large at a height from the optical axis as possible. This is based on the following fact. Letting .nu. denote the lens surface number, h.nu. the height from the optical axis of a point of incidence of an axial light ray on the corresponding lens surface, and h.nu. the height from the optical axis of a point of incidence of a diaphragm-centered off-axis principal light ray on the corresponding lens surface, we have the degrees of contribution of a non-spherical surface formed in an optionally selected one to various aberrations in terms of three-order aberration coefficients, namely, spherical aberration I = .SIGMA.I.nu., coma II = .SIGMA.II.nu., astigmatism III = .SIGMA.III.nu., and distortion V = .SIGMA.V.nu., as being proportional to h.nu..sup.4 for I.nu., h.nu..sup.3 h.nu. for II.nu., h.nu..sup.2 h.nu..sup.2 for III.nu., and h.nu.h.nu..sup.3 for V.nu.. These relationships suggest that when a non-spherical surface is employed in correcting for distortion while minimizing its influence on other aberrations, a surface having a larger h.nu. and simultaneously having a smaller h.nu. must be selected for non-spherical configuration.
In the case of a retrofocus wide angle lens system comprising from front to rear a diverging first component, a converging second component, a diaphragm, and a converging third component, it is usual that the surface having the largest h.nu. and small h.nu. is located in the first component.
Even in fifth order and higher order region, it is true that the non-spherical surface operates for distortional correction effectively at a location where h.nu. is larger. For facilitating correction of distortion in the aforesaid type lens system, it is preferred that the first lens component is provided with at least one non-spherical surface.
On the other hand, for the primary purpose of paralleling the practices used in manufacturing the lens elements under an economical production run, the surface having the largest h.nu. is not always selected for non-spherical configuration. But, even in this case, the location of the non-spherical surface is limited within the first lens component. With the first lens component with the rearmost surface, for example, being configured to non-spherical, it is possible to achieve good correction for distortion provided either that the number of concave lens elements in the first component is increased with extreme bending as convex toward the front, or that the number of convex lens elements is increased to effect under-correction of distortion to some extent.
The rectangular co-ordinates X and H for expression of the non-spherical surface are given below ##EQU1## wherein X is the co-ordinate of which the axis coincides with the optical axis of the system and which is given the positive sign when it falls to the direction of incident light rays under the assumption that the non-spherical surface intersects the optical axis at its vertex as coincident with the original point; H is the co-ordinate perpenducular to the optical axis; R is the radius of curvature of the non-spherical surface in the paraxial region; and A to E are non-spherical coefficients. Of these non-spherical coefficients, B shall be given the positive sign when the non-spherical surface is convex to the front and given the negative sign when it is concave to the front.
It will be seen from the foregoing that the introduction of such a non-spherical surface to the lens system for the primary purpose of correcting distortion is entirely unfree from also influencing at the same time in an undesirable manner the correction for other aberrations since astigmatism is most strongly deteriorated. This problem becomes serious when the lens system is of the type referred to and to which the present invention relates, as the distortion is under-corrected by the introduction of the non-spherical surface to extremely large extent but within the acceptable range so that the resulting astigmatism is extremely undercorrected. For this reason, a new method must be developed to compensate for this extremely under-corrected astigmatism without causing deterioration of the other aberrations.